As the sample size increases the standard deviation of the sample decreases and hence the variability of the sample decreases. Option B is correct.
What is the standard deviation?
The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers.
i) Let the standard deviation of the population be given by σ.
ii) For the sample taken from among the population of size n the standard deviation of the sample becomes and so we can see that for the sample the standard deviation of the sample is less than the standard deviation of the sample.
iii) As the sample size increases we can say that the standard deviation of the sample decreases.
iv) The variance, or variability, of a sample is equal to the square of the standard deviation of the sample.
Therefore, as the sample size increases the standard deviation of the sample decreases, and hence the variability of the sample decreases.
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